200

ELECTRICAL APPARATUS

• 1

external circuit is /o — fa, hence equals fi, or the stator frequency. •
Stator and rotor so give the same effective frequency, /i, and
irrespective of the frequency, /2 generated in the rotor, and the
frequencies, /i and /2, accordingly become indefinite, that is,
/i may be any frequency, fz then becomes /0 — /i, but by the
commutator is transformed to the same frequency, /i. If the
stator and rotor were used on entirely independent electric
circuits, the frequency would remain indeterminate. As soon,
however, as stator and rotor are connected together, a relation
appears due to the transformer law, that the secondary ampere-
turns must equal the primary ampere-turns (when neglecting
the exciting ampere-turns) . This makes the frequency dependent
upon the number of turns of stator and rotor circuit.

Assuming the rotor circuit is connected in multiple with the
stator circuit — as it always can be, since by the commutator
brushes it has been brought to the same frequency. The rotor
e.m.f. then must be equal to the stator e.m.f. The e.m.f., how-
ever, is proportional to the frequency times number of turns,
and it is therefore:

where :

HI = number of effective stator turns,

n2 = number of effective rotor turns, and

and/2 are the respective frequencies.
Heref rom follows :

that is, the frequencies are inversely proportional to the number
of effective turns in stator and in rotor.

Or, since /o = f\ + /2 is the frequency of rotation :

/! =

+

That is, the frequency, /i, generated by the synchronous-
induction machine with commutator, is the frequency of rotation,
/o, times the ratio of rotor turns, n^ to total turns, ni + n^
Thus, it can be made anything by properly choosing the
number of turns in the rotor and in the stator, or, what amounts
to the same, interposing between rotor and stator a transformer
of the proper ratio of transformation.